In the beginning a Roman legion was the whole of the army:

The latin word
legio means army and that was what the army was, initially.
But a larger army than one
single legion became
needed, when Rome grew and found
evermore powerful enemies.
The smallest unit was the century, commanded
by a centurion. The centurion was an experienced soldier who had proven
to be brave but not reckless. His second in command was the optio. His
place was in the back of the century, to keep the men in place.

A century consisted of 60 legionnaires of the same kind. I.e. All
hastati or principii or triarii. This number was not really fixed and
could be expanded to 120 in times of crisis. A century of triarii
consisted of
only 30 legionnaires. This number was never changed.

Important figure in the century was the signifer, who bore the the
standard of the century. Losing the standard in a battle would
mean loosing the honour of the unit.
Livius 3.70:

The right wing gave more trouble. Here Agrippa, whose age and strength made
him fearless, seeing that things were going better in all parts of the
field than with him, seized standards from the standard-bearers and
advanced with them himself, some he even began to throw amongst the
masses of the enemy. Roused at the fear and disgrace of losing them,
his men made a fresh charge on the enemy, and in all directions the
Romans were equally successful.

Two centuries of the same kind formed a manipel. The centurion of the
right century was also the commander of the manipel. The manipel was
the lowest tactical unit of the roman army.